# Properties

 Label 3600.1.e Level $3600$ Weight $1$ Character orbit 3600.e Rep. character $\chi_{3600}(3151,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $4$ Sturm bound $720$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3600.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$720$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3600, [\chi])$$.

Total New Old
Modular forms 90 6 84
Cusp forms 18 6 12
Eisenstein series 72 0 72

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6 q + O(q^{10})$$ $$6 q + 2 q^{13} + 2 q^{29} - 2 q^{37} + 2 q^{41} - 6 q^{49} - 4 q^{61} + 2 q^{73} + 2 q^{89} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3600, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3600.1.e.a $1$ $1.797$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{29}+2q^{41}+q^{49}-2q^{61}+2q^{89}+\cdots$$
3600.1.e.b $1$ $1.797$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{13}-2q^{37}+q^{49}+2q^{61}+2q^{73}+\cdots$$
3600.1.e.c $2$ $1.797$ $$\Q(\sqrt{-3})$$ $D_{6}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$$
3600.1.e.d $2$ $1.797$ $$\Q(\sqrt{-3})$$ $D_{6}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3600, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3600, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(400, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(900, [\chi])$$$$^{\oplus 3}$$